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# Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient# Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient# BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient# EACH statement ALONE is sufficient# Statements (1) and (2) TOGETHER are NOT sufficient
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# Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient# Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient# BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient# EACH statement ALONE is sufficient# Statements (1) and (2) TOGETHER are NOT sufficient

Question Stem : What is the cost of 5 pencils?Let p refer to price of one pencil and q refer to price of one pen.We are given that both p and q must be non zero whole numbers (1,2,3,4,5.... and so on).

St. (1) : 5p + 3q = 30This can be written as \(p = \frac{30-3q}{5} = 6 - \frac{3q}{5}\)This implies that in order for p to be a whole number, q must be a multiple of 5. Also, we can see that if q = 10, then p will be equal to 0. Since this cant be possible, q must be less than 10. Also, since q itself cant be 0, it must be greater than 0. The only multiple of 5 that satisfies this condition is the number 5 itself.

Thus we get q = 5 and p = 3.

Statement is sufficient.

St. (2) : 4p + 4q = 32This can be written as p + q = 8Thus, since different sets of values of p and q can satisfy this condition, it cannot be sufficient.

Answer : A_________________

Click below to check out some great tips and tricks to help you deal with problems on Remainders! http://gmatclub.com/forum/compilation-of-tips-and-tricks-to-deal-with-remainders-86714.html#p651942